System Theoretic Study on Learning Control Method

摘要

High speed motion and accurate positioning of robots can not be obtained simply by applying the desired trajectory to each servo system, because of the dynamic interfernces. To overcome this difficulty we apply a kind of learning control which uses the iteration of motion. In this control scheme, a refernce trajectory is corrected by considering the error in every trial so that the system response can accurately coincide with desired trajectory.This type of learning control system was first investigated by Uchiyama (1978)1. It dealt with a single-input and single-output system, and theoretic properties of learning control are not made clear. In this paper, the stability of learning control for multi-input and multi-output systems is discussed and it is shown that the following three conditions are equivalent each other:(1) stability of learning control(2) bounded real property(3) sensitivity reduction (optimal regulator)From this relation among conditions, it is shown that an optimal regulator system is stable in the sense of learning control and the feedback gains which satisfy the stability of learning control can easily be determined by solving the Riccati matrix equation. Moreover, it is proved that the learning control is considered to be a process of constructing an inverse system.According to some computer simulations, it is shown that a choice of some system parameters (e. g. feedback gains and cost function) extremely changes the performance of learning control.